All entries in the Csagrid package have a parameter that designates the number of knots to use in each of the coordinate directions. The package automatically spaces the knots evenly from the minimum value to the maximum value in each coordinate direction. In each coordinate direction, the number of knots must be at least 4 and at most equal to the number of input data values. The more knots that are specified, the closer the approximation will fit the original data, at the expense of compute time. See the plot for Example 1 for an illustration of how the number of knots affects an approximated curve. See the timing table for how the number of knots affects compute time.
The entries in the expanded interface of Csagrid contain a parameter to control extrapolation to data sparse regions. If this parameter is set to a positive value, certain derivative constraints are used to extrapolate into data sparse regions before the approximation function values are calculated. This tends to smooth out the unexpected oscillations (larger values for the extrapolation parameter yield greater smoothing, but frequently the differences are subtle). The bottom curve in the plot for Example 3 illustrates setting the extrapolation parameter to "1." and offers a comparison with a curve produced using the same input data, but without the extrapolation parameter set (the top curve in the plot for Example 3).
The practical implication of this is that if you see an unexpected oscillation in your output curve or surface, analyze whether that is occurring in a data sparse region and, if so, set the extrapolation parameter to a positive value (experience has indicated that choosing "1." is a good start) and see if the result is more reasonable.
Note: Extrapolating into data sparse regions greatly alters the computation of first and second derivatives to the point where they are effectively meaningless.